• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.849-862
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• 2011

In this paper, we introduce certain concepts which provide us with a perspective and insight into the generalization of orthogonality with the normalized duality mapping. The material of this paper will be mainly, but not only, used in developing algorithms for the best approximation problem in a Banach space.

• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.69-76
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• 2007

Let $f$ denote a mapping from an orthogonality space ($\mathcal{X}$, ${\bot}$) into a real Banach space $\mathcal{Y}$. In this paper, we prove the Hyers-Ulam-Rassias stability of the orthogonally cubic functional equations $f(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x)$ and $f(x+y+2z)+f(x+y-2z)+f(2x)+f(2y)=2f(x+y)+4f(x+z)+4f(x-z)+4f(y+z)+4f(y-z)$, where $x{\bot}y$, $y{\bot}z$, $x{\bot}z$.

• Korean Journal of Mathematics
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• v.20 no.1
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• pp.77-89
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• 2012

Using fixed point method, we prove the Hyers-Ulam stability of the orthogonally additive functional equation (0.1) $f(2x+y)=2f(x)+f(y)$ and of the orthogonally quadratic functional equation (0.2) $2f(\frac{x}{2}+y)+2f(\frac{x}{2}-y)=f(x)+4f(y)$ for all $x$, $y$ with $x{\perp}y$ in orthogonality spaces.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.377-391
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• 2013

The main goal of this paper is to present the additional stability results of the following orthogonally additive and orthogonally quadratic functional equation $$f(\frac{x}{2}+y)+f(\frac{x}{2}-y)+f(\frac{x}{2}+z)+f(\frac{x}{2}-z)=\frac{3}{2}f(x)-\frac{1}{2}f(-x)+f(y)+f(-y)+f(z)+f(-z)$$ for all $x,y,z$ with $x{\bot}y$, which has been introduced in the paper [11], in orthogonality Banach spaces and in non-Archimedean orthogonality Banach spaces.

• Korean Journal of Mathematics
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• v.20 no.1
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• pp.33-46
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• 2012

Using the direct method, we prove the Hyers-Ulam stability of the orthogonally additive-quartic functional equation (0.1) $f(2x+y)+f(2x-y)=4f(x+y)+4f(x-y)+10f(x)+14f(-x)-3f(y)-3f(-y)$ for all $x$, $y$ with $x{\perp}y$, in non-Archimedean Banach spaces. Here ${\perp}$ is the orthogonality in the sense of R$\ddot{a}$tz.

• Korean Journal of Mathematics
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• v.21 no.1
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• pp.1-21
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• 2013

Using the fixed point method, we prove the Ulam-Hyers stability of the orthogonally additive and orthogonally quadratic functional equation $$f(\frac{x}{2}+y)+f(\frac{x}{2}-y)+f(\frac{x}{2}+z)+f(\frac{x}{2}-z)=\frac{3}{2}f(x)-\frac{1}{2}f(-x)+f(y)+f(-y)+f(z)+f(-z)$$ (0.1) for all $x$, $y$, $z$ with $x{\bot}y$, in orthogonality Banach spaces and in non-Archimedean orthogonality Banach spaces.

• ETRI Journal
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• v.45 no.2
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• pp.203-212
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• 2023

In this study, we developed a co-located and space-shared multiple-input multiple-output (MIMO) antenna module with a modular design and high integration level. The proposed antenna pair includes a half-wavelength loop antenna and a dipole-type antenna printed on the front and back sides of a compact modular board. Owing to their modal orthogonality, these two independent antenna elements are highly self-isolated and free of additional decoupling components, even though they are assembled at the same location and within the same space. Thus, the proposed antenna is attractive in 5G MIMO systems. Furthermore, the proposed co-located and space-shared MIMO antenna module was employed in a 5G smartphone to verify their radiation and diversity performances. A 12 × 12 MIMO antenna system was simulated and fabricated using the proposed module. Based on the results, the proposed module can be employed in large-scale MIMO antenna systems for current and future terminal devices owing to its high integration, compactness, simple implementation, and inherent isolation.

• Proceedings of the IEEK Conference
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• 1998.06a
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• pp.211-214
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• 1998

A detection filter assigns a specific direction to the response with respect to each fault, by which it can detect the occurrence of the several faults. The separability of a detection filter can be determined by the orthogonality among these directions. In this paper, we define the separability of a detection filter as the orthogonality of the directions in output space, and present it mathematically by using conditions number. An algorithm to determine the optimal sensor gain to maximize separability is proposed and applied to the PWR nuclear reactor model.

• East Asian mathematical journal
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• v.31 no.5
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• pp.627-634
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• 2015

In this paper, we investigate the following orthogonally additive-quadratic functional equation f(2x + y) - f(x + 2y) - f(x + y) - f(y - x) - f(x) + f(y) + f(2y) = 0. and prove the generalized Hyers-Ulam stability for it in orthogonality spaces by using the fixed point method.

• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.601-606
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• 2008

The purpose of this paper is to introduce and discuss the concept of ${\omega}$-Chebyshev subspaces in Banach spaces. The concept of quasi Chebyshev in Banach space is defined. We show that ${\omega}$-Chebyshevity of subspaces are a new class in approximation theory. In this paper, also we consider orthogonality in normed spaces.